Data 605 Homework Week-5

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Student Name : Sachid Deshmukh

Date : 02/27/2019

• GitHub Location for rmd file

• RPubs location of published file

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Choose independently two numbers B and C at random from the interval [0, 1] with uniform density. Prove that B and C are proper probability distributions.Note that the point (B,C) is then chosen at random in the unit square.

Let’s simulate B and C using uniform distribution function

# Take sample of 1000 random numbers from uniform distribution with min = 0 and max =1

B = runif(1000, min=0, max=1 )
C = runif(1000, min=0, max=1 )

1. Find the probability that B+C < 0.5

result = B + C
print(length(result[result < 0.5])/length(result))

## [1] 0.12

2. Find the probability that BXC < 0.5

result = B * C
print(length(result[result < 0.5])/length(result))

## [1] 0.844

3. Find the probability that ABS(B-C) < 0.5

result = abs(B - C)
print(length(result[result < 0.5])/length(result))

## [1] 0.741

4. Find the probability that MAX(B, C) < 0.5

result = pmax(B, C)
print(length(result[result < 0.5])/length(result))

## [1] 0.231

5. Find the probability that MIN(B, C) < 0.5

result = pmin(B, C)
print(length(result[result < 0.5])/length(result))

## [1] 0.749